I hate to say "the sense of accomplishment", because everyone with half a brain knows that playing a video game doesn't equate to accomplishing jack shit, but for me and a lot of my friends, that was the main draw. The game would always give us something to work towards, and we delighted in putting in the grind every day to get a little bit closer to the shiny horse or armor set or whatever.
The really sinister thing about MMOs, however, is how they overshadow everything else that you used to enjoy doing. The genre is not designed to reward short intervals of playtime; everything is on such a grandiose scale that you don't feel like you've really played unless you put in a lot of hours every day. Before you know it, you find yourself reflexively opening your MMO of choice as soon as the computer boots, and touching nothing else, save for something like background music. The game then stays open until you finally pry yourself away to do something more important, usually work or sleep. Worse still, when you run out of interesting things to do, you just brainlessly do the unfun shit because at least you're doing something. When you finally run out of objectives on one character, you just start a new one and begin the whole thing again.
Others in this thread have mentioned the social aspect, which does exist. However, in my experience, eventually my friends' conversations devolved entirely into WoW shit. We would seldom bring up something unrelated, but for the most part, it was shit about the game, followed by varied periods of silence. Any time a new person entered our circle and/or guild, we would shoot the shit with them at first, but eventually the curiosity wore off and we were back to talking about the same mundane game-related things. My friends and I stopped meeting IRL as often, and when we did meet up, the conversation would be about the game, like we hadn't even left our houses.
I can't say for sure whether I was ever addicted, because I never felt any kind of withdrawal symptoms when I decided to stop playing for whatever reason, but I definitely noticed how much of my time I had been putting in, and how much more time I seemed to have for other things when I stopped.
TL;DR: A lot of nerds play MMOs because they make you work for something long enough that by the time you get it, you feel some contrived sense of accomplishment.